Global attractors for the 2D hyperbolic Cahn–Hilliard equations

Abstract

We consider the initial boundary value problem for the hyperbolic relaxation of the 2D Cahn–Hilliard equation with sub-cubic nonlinearity. Under mild regularity conditions on the nonlinearity, we prove the uniform (with respect to the initial data) boundedness of the weak solutions without assuming lower bound condition on the first derivative of the nonlinear term. Then, we prove the existence of the regular global attractor for the weak solutions.